Yes. PixtaSynapse has been built with the concept of "Permissions" for each user. Go to ‘Account Settings->Users’ and set up as many users for the account as you need. Here you can easily assign them permissions to download, delete files, change account settings etc.
If you account name is ‘bigsigns’ a user, sarah, for you account then signs on as:
The account administrator can set-up as many users as you need and assign unique roles to each to match the account details the account administrator exposes to them.